A non-implication between fragments of Martin’s Axiom related to a property which comes from Aronszajn trees

Annals of Pure and Applied Logic 161 (4):469-487 (2010)
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Abstract

We introduce a property of forcing notions, called the anti-, which comes from Aronszajn trees. This property canonically defines a new chain condition stronger than the countable chain condition, which is called the property . In this paper, we investigate the property . For example, we show that a forcing notion with the property does not add random reals. We prove that it is consistent that every forcing notion with the property has precaliber 1 and for forcing notions with the property fails. This negatively answers a part of one of the classical problems about implications between fragments of

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10.1016/j.apal.2009.02.006

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Citations of this work

The relative strengths of fragments of Martin's axiom.Joan Bagaria - 2024 - Annals of Pure and Applied Logic 175 (1):103330.
Club-Isomorphisms of Aronszajn Trees in the Extension with a Suslin Tree.Teruyuki Yorioka - 2017 - Notre Dame Journal of Formal Logic 58 (3):381-396.

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Internal cohen extensions.D. A. Martin & R. M. Solovay - 1970 - Annals of Mathematical Logic 2 (2):143-178.
Internal Cohen extensions.D. A. Martin - 1970 - Annals of Mathematical Logic 2 (2):143.

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